What is the derivative of ((x+4(x^2-4x+16))/(x^3)) ?

The derivative of ((x+4(x^2-4x+16))/(x^3)) is -(192)/(x^4)

What is the first derivative of ((x+4(x^2-4x+16))/(x^3)) ?

The first derivative of ((x+4(x^2-4x+16))/(x^3)) is -(192)/(x^4)

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\frac{d}{d x} (\frac{( x + 4 ) ( x ^{2} - 4 x + 16 )}{x ^{3}})

- \frac{192}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{( x + 4 ) ( x ^{2} - 4 x + 16 )}{x ^{3}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ( x + 4 ) ( x ^{2} - 4 x + 16 ) ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( x + 4 ) ( x ^{2} - 4 x + 16 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} ((x + 4) (x^{2} - 4 x + 16)) = 3 x^{2}

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x + 4 ) ( x ^{2} - 4 x + 16 )}{( x ^{3} ) ^{2}}

Simplify

\frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x + 4 ) ( x ^{2} - 4 x + 16 )}{( x ^{3} ) ^{2}} : - \frac{192}{x ^{4}}

= - \frac{192}{x ^{4}}

5 x sin (x)

\int e^{- x} - 1 d x

\frac{\partial}{\partial x} (- x^{2})

\frac{\partial ^{2}}{\partial r \partial θ} (r (θ) \cdot sin (θ))

y = 2 x^{4}, (- 2, 32)

What is the derivative of ((x+4(x^2-4x+16))/(x^3)) ?
The derivative of ((x+4(x^2-4x+16))/(x^3)) is -(192)/(x^4)
What is the first derivative of ((x+4(x^2-4x+16))/(x^3)) ?
The first derivative of ((x+4(x^2-4x+16))/(x^3)) is -(192)/(x^4)